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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
There are $4$ books on fairy tales, $5$ novels and $3$ plays. In how many ways can they be arranged in the order books on fairy tales, novels and then plays so that books of same category are put together
Solution
Given:$4$ books on fairy tales, $5$ novels, $3$ plays
The order of arrangement is fixed as:
Fairy Tales $\rightarrow$ Novels $\rightarrow$ Plays
Step 1: Arrange books within each category
Fairy tales books can be arranged among themselves $= 4!= 24$ ways
Novels can be arranged among themselves $= 5! = 120$ ways
Plays can be arranged among themselves $= 3! = 6$ ways
Step 2: Total number of arrangements
$= 4! \times 5! \times 3!$
$= 24 \times 120 \times 6$
$\therefore \boxed{= 17280 \text{ ways}}$
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